Mathematical Sciences: Representations of Forms in Several Variables

数学科学：多变量形式的表示

• 批准号: 9204126
• 负责人: Bruce Reznick
• 金额: $ 8.82万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-15 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204126&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Representations; Forms; Several

This research is concerned with the study of real and complex forms by means of a natural inner product. The principal investigator will examine sums of even powers of forms; spherical designs; sums of powers of complex linear forms; sums of cubes of linear forms; inequalities for products of forms; and symmetric forms. The research supported involves the theory of forms. This is the study of homogeneous polynomials over the real numbers or over the complex numbers. The study of real and complex forms has deep interrelations with linear algebra, combinatorics, number theory, algebraic geometry, functional analysis and numerical analysis.

本研究关注的是对真实的和复杂的 它是由自然的内部产品形成的。 校长 研究者将检查形式的偶数幂的总和;球形的 设计;复线性形式的幂和; 线性形式;形式乘积的不等式;对称 forms. 支持的研究涉及形式理论。 这是 研究真实的数上的齐次多项式 复数 对真实的和复杂形式的研究具有深刻的意义。 与线性代数、组合学、数论的相互关系， 代数几何、泛函分析和数值分析。